3. (a) (6 pts) Find the linearization of \( f(x)=\sqrt{x} \) at \( x=25 \). (b) (4 pts) Use your answer to part (a) to find a linear approximation of \( \sqrt{25.046} \). Write your answer to at least four decimal places.
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The linearization of a function \(f(x)\) at a point \(x = a\) is the tangent line to the function at that point. The equation of this line can be found using the formula \(L(x) = f(a) + f'(a)(x - a)\), where \(f'(a)\) is the derivative of \(f(x)\) evaluated at \(x Show more…
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